Population-based meta-heuristic is a high-level method intended to provide sufficient solution for problems with incomplete information among a massive volume of solutions. However, it does not guarantee to attain global optimum in a reasonable time. To improve the time and accuracy of the coverage in the population-based meta-heuristic, this paper presents a novel algorithm called the raccoon optimization algorithm (ROA). The ROA is inspired by the rummaging behaviors of real raccoons for food. Raccoons are successful animals because of their extraordinarily sensitive and dexterous paws and their ability to find solutions for foods and remember them for up to three years. These capabilities make raccoons expert problem solvers and allow them to purposefully seek optimum solutions. These behaviors exploited in the ROA to search the solution spaces of nonlinear continuous problems to find the global optimum with higher accuracy and lower time coverage. To evaluate the ROA’s ability in addressing complicated problems, it has been tested on several benchmark functions. The ROA is then compared with nine other well-known optimization algorithms. These experiments show that the ROA achieves higher accuracy with lower coverage time.

We consider pursuit‐evasion differential game of countable number inertial players in Hilbert space with integral constraints on the control functions of players. Duration of the game is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the functional, and the evader tries to maximize it. In this paper, we find the value of the game and construct optimal strategies of the players.

An evasion differential game of one evader and many pursuers is studied. The dynamics of state variables $$x_1,\ldots , x_m$$x 1 , … , x m are described by linear differential equations. The control functions of players are subjected to integral constraints. If $$x_i(t) \ne 0$$x i ( t ) ≠ 0 for all $$i \in \{1,\ldots ,m\}$$i ∈ { 1 , … , m } and $$t \ge 0$$t ≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn’t exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible.

We study a simple motion pursuit differential game of many pursuers and many evaders on a nonempty convex subset of ℝⁿ. In process of the game, all players must not leave the given set. Control functions of players are subjected to integral constraints. Pursuit is said to be completed if the position of each evader y_j, j ∈ {1, 2, …k}, coincides with the position of a pursuer x_i, i ∈ {1, …, m}, at some time t_j, that is, x_i(t_j) = y_j(t_j). We show that if the total resource of the pursuers is greater than that of the evaders, then pursuit can be completed. Moreover, we construct strategies for the pursuers. According to these strategies, we define a finite number of time intervals [θ_i−1, θ_i] and on each interval only one of the pursuers pursues an evader, and other pursuers do not move. We derive inequalities for the resources of these pursuer and evader and, moreover, show that the total resource of the pursuers remains greater than that of the evaders.